Chinese remainder theorem
Let be a commutative ring with identity. If are ideals of such that whenever , then let
The sum of quotient maps gives an isomorphism
This has the slightly weaker consequence that given a system of congruences , there is a solution in which is unique mod , as the theorem is usually stated for the integers.
Title | Chinese remainder theorem |
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Canonical name | ChineseRemainderTheorem1 |
Date of creation | 2013-03-22 12:16:43 |
Last modified on | 2013-03-22 12:16:43 |
Owner | bwebste (988) |
Last modified by | bwebste (988) |
Numerical id | 7 |
Author | bwebste (988) |
Entry type | Theorem |
Classification | msc 11N99 |
Classification | msc 11A05 |
Classification | msc 13A15 |
Related topic | ChineseRemainderTheoremInTermsOfDivisorTheory |